This artifact contains the Coq formalization associated with the paper The Duality of Subtyping submitted in ECOOP 2020. This document explains how to run the Coq formalization. Artifact can either be compiled in the pre-built docker image with all the dependencies installed or it could be built from the scratch. Sections 1-7 explain the basic information about the artifact. Section A explains how to get the docker image for the artifact. Section B explains the prerequisites and the steps to run coq files from scratch. Section C explains coq files briefly. Section D shows the correspondence between important lemmas discussed in paper and their respective Coq formalization. The term MonoTyping used in artifact corresponds to the standard subtyping systems

Oliveira, Bruno C. d. S.

Rehman, Baber

Shaobo, Cui

English

Dagstuhl Research Online Publication Server

The Duality of Subtyping (Artifact)Bruno C. d. S. OliveiraThe University of Hong Kong, Chinabruno@cs.hku.hkCui ShaoboUniversity of California San Diego, CA, USAcuishaobo@gmail.comBaber RehmanThe University of Hong Kong, Chinabrehman@cs.hku.hkAbstractThis artifact contains the Coq formalization associ-ated with the paper The Duality of Subtypingsubmitted in ECOOP 2020. This document ex-plains how to run the Coq formalization. Artifactcan either be compiled in the pre-built docker im-age with all the dependencies installed or it couldbe built from the scratch. Sections 1-7 explain thebasic information about the artifact. Section A ex-plains how to get the docker image for the artifact.Section B explains the prerequisites and the stepsto run coq files from scratch. Section C explainscoq files briefly. Section D shows the correspond-ence between important lemmas discussed in paperand their respective Coq formalization. The termMonoTyping used in artifact corresponds to thestandard subtyping systems.2012 ACM Subject Classification Software and its engineering → Object oriented languagesKeywords and phrases DuoTyping, OOP, Duality, Subtyping, SupertypingDigital Object Identifier 10.4230/DARTS.6.2.8Funding Funded by Hong Kong Research Grant Council projects number 17210617 and 17209519.Acknowledgements We thank the anonymous reviewers for their helpful comments.Related Article Bruno C. d. S. Oliveira, Cui Shaobo, and Baber Rehman, “The Duality of Subtyping”,in 34th European Conference on Object-Oriented Programming (ECOOP 2020), LIPIcs, Vol. 166,pp. 29:1–29:29, 2020. https://doi.org/10.4230/LIPIcs.ECOOP.2020.29Related Conference 34th European Conference on Object-Oriented Programming (ECOOP 2020),November 15–17, 2020, Berlin, Germany (Virtual Conference)1 ScopeThis artifact contains the Coq formalization associated with the paper The Duality of Subtypingsubmitted in ECOOP 2020. We provide the Coq formalization of various standard subtyping andour Duotyping systems.2 ContentThe artifact package includes:MonoTyping Coq FormalizationDuoTyping Coq FormalizationCopy of related paper (The Duality of Subtyping)README file with compilation instructions© Bruno C. d. S. Oliveira, Cui Shaobo, and Baber Rehman;licensed under Creative Commons Attribution 3.0 Germany (CC BY 3.0 DE)Dagstuhl Artifacts Series, Vol. 6, Issue 2, Artifact No. 8, pp. 8:1–8:6Dagstuhl Artifacts SeriesSchloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany8:2 The Duality of Subtyping (Artifact)3 Getting the artifactThe artifact endorsed by the Artifact Evaluation Committee is available free of charge on theDagstuhl Research Online Publication Server (DROPS). In addition, the artifact is also availableat: https://github.com/baberrehman/coq-duotyping.4 Tested platformsThe artifact has been tested using Coq 8.7.0.5 LicenseThe artifact is available under license BSD.6 MD5 sum of the artifact5dcbcfceaba4c767a6dd8611b6320c867 Size of the artifact797.0 KBA Docker ImageThis section explains how to pull the docker image of artifact from docker hub and use it. Runthe following commands one by one in terminal:1. $ docker pull baberrehman/duotyping2. $ docker run -it baberrehman/duotyping3. $ eval $(opam env)The artifact is located in /home/coq/coq-duotyping/coq/ directory.There are two folders in the artifact, with make file in each:1. MonoTyping → contains traditional subtyping formulation2. DuoTyping → contains our duotyping formulationGo to each folder and run make:1. $ cd /home/coq/coq-duotyping/coq/DuoTyping2. $ eval $(opam env)3. $ makecoqc GStlc.vcoqc GStlcExtra .vcoqc GUnionInter .vcoqc GUnionInterExtra .vcoqc GFSubKernel .vcoqc GFSubKernelExtra .vcoqc GFSubKernelUnionInter .vcoqc GFSubKernelUnionInterExtra .vcoqc GFSubFull .vcoqc GFSubFullExtra .vB.C. d. S. Oliveira, C. Shaobo, and B. Rehman 8:31. $ cd /home/coq/coq-duotyping/coq/MonoTyping2. $ eval $(opam env)3. $ makecoqc STLCSub .vcoqc STLCSubUnionInter .vcoqc FSubKernal .vcoqc FSubKernalUnionInter .vcoqc FSub.vB Build from ScratchThis section explains how to build the artifact from scratch.B.1 PrerequisitesWe tested all the Coq files using Coq version 8.7.0. Please use same version for the sake ofconsistency. We recommend installing Coq using the opam package installer.Run the following command to install Coq via opam:$ opam install coq.8.7.0Refer to this link for more information and installation steps:https://coq.inria.fr/opam-using.htmlB.2 Required LibrariesCoq TLC library release 20181116 is also required to compile the code. TLC library can also beinstalled using the opam package installer.Run the following commands one by one to install TLC by opam package installer:1. $ opam repo add coq-released http://coq.inria.fr/opam/released2. $ opam install coq-tlc.20181116Please refer to this link for detailed compilation and installation of Coq TLC:https://gitlab.inria.fr/charguer/tlc/-/blob/20181116/README.mdUser should be able to run each file individually using Coqide if these dependencies are installed.B.3 Getting the artifactUse the following commands to clone our git repo. Please note that $ symbol is not a part ofcommand:$ git clone https://github.com/baberrehman/coq-duotyping.gitAlternatively you can download the zip file from repo and you should be able to see all the Coqfiles after unzipping it.DARTS8:4 The Duality of Subtyping (Artifact)B.4 Proof StructureThere are two folders in the artifact, docs and coq. Folder coq contains all the Coq files. Coqfiles are further divided into categories with separate folders:1. MonoTyping → contains traditional subtyping formulation2. DuoTyping → contains our duotyping formulationB.5 CompilationPlease make sure to run the following command before running make if you installed the Coq viaopam:$ eval $(opam env)Makefiles are available in both MonoTyping and DuoTyping folder. Run make commandindividually in each folder to compile.B.6 PaperYou can also find a copy of our ECOOP’20 paper (The Duality of Subtyping) in docs folder.C Overview of Coq FilesThis section explains all the Coq files of our Duotyping systems and the traditional subtypingsystems that we formalized. Table 1 shows the correspondence of Coq files and the respectivesystems. For example, one can find the Coq code for the system λ<:in file Monotyping/STLCSub.v.We consider coq folder in unzipped artifact directory as reference point. We have both, algorithmicand the declarative formulation for all the Duotyping systems. The Coq formalizations for thetraditional subtyping systems are based on existing Coq formalizations from the locally namelessrepresentation with cofinite quantification tutorial and repository (https://www.chargueraud.org/softs/ln/) by Charguéraud [1]. The formalizations of λ♦, λ∧∨♦ , Fk♦, F∧∨k♦ and FF♦are theirrespective Duotyping formulations, and modify the original ones with traditional subtyping.D Overview of Important LemmasThis section briefly explains the important lemmas discussed in paper and their correspondencewith the coq formulation. Table 2 shows the correspondence between lemmas discussed in paperand their source coq code. For example, one can find the Lemma 1 (λ<:Transitivity) in fileMonotyping/STLCSub.v and the lemma name in file is sub_transitivity.References1 Arthur Charguéraud. The locally nameless repres-entation. Journal of Automated Reasoning, 2011.B.C. d. S. Oliveira, C. Shaobo, and B. Rehman 8:5Table 1 Description of Coq files of all systems.Name Description Coq Fileλ<: STLC with subtyping Monotyping/STLCSub.vλ♦ STLC with Duotyping (Algorithmic) DuoTyping/GStlc.vλ♦ STLC with Duotyping (Declarative) DuoTyping/GStlcExtra.vλ∧∨<: STLC with subtyping, union and intersec-tion typesMonotyping/STLCSubUnionInter.vλ∧∨♦ STLC with Duotyping, union and intersec-tion types (Algorithmic)DuoTyping/GUnionInter.vλ∧∨♦ STLC with Duotyping, union and intersec-tion types (Declarative)DuoTyping/GUnionInterExtra.vFk<: System F<: kernel Monotyping/FSubKernal.vFk♦ System F<: kernel with Duotyping (Al-gorithmic)DuoTyping/GFSubKernel.vFk♦ System F<: kernel with Duotyping (Declar-ative)DuoTyping/GFSubKernelExtra.vF∧∨k<: System F<: kernel with union and intersec-tion typesMonotyping/FSubKernalUnionInter.vF∧∨k♦ System F<: kernel with Duotyping, unionand intersection types (Algorithmic)DuoTyping/GFSubKernelUnionInter.vF∧∨k♦ System F<: kernel with Duotyping, unionand intersection types (Declarative)DuoTyping/GFSubKernelUnionInterExtra.vFF <: System full F<: Monotyping/FSub.vFF♦ System full F<: with Duotyping (Al-gorithmic)DuoTyping/GFSubFull.vFF♦ System full F<: with Duotyping (Declarat-ive)DuoTyping/GFSubFullExtra.vDARTS8:6 The Duality of Subtyping (Artifact)Table 2 Overview of important lemmas.Lemma in Paper Coq File Lemma in CoqFileLemma 1 (λ<:Transitivity) Monotyping/STLCSub.v sub_transitivityLemma 2 (λ♦Transitivity) DuoTyping/GStlc.v transTheorem 1 (Reflexivity) DuoTyping/GUnionInter.v reflTheorem 2 (Transitivity) DuoTyping/GUnionInter.v transLemma 1 (Bound Selection) DuoTyping/GUnionInter.v invBoundLemma 2 (Inversion for ruleGDS-Both)DuoTyping/GUnionInter.v invChooseLemma 3 (Inversion forUnion types)Monotyping/STLCSubUnionInter.v invOrS1Lemma 4 (Inversion for In-tersection types)Monotyping/STLCSubUnionInter.v invAndS1Lemma 3 (Duality) DuoTyping/GUnionInter.v sym1Lemma 5 (Type Preserva-tion)DuoTyping/GUnionInter.v preservation_resultLemma 6 (Progress) DuoTyping/GUnionInter.v progress_resultTheorem 3 (Reflexivity) DuoTyping/GFSubKernelUnionInter.v reflTheorem 4 (Transitivity) DuoTyping/GFSubKernelUnionInter.v sub_transitivityLemma 7 (Bound Selection) DuoTyping/GFSubKernelUnionInter.v TopBtmMustEq1Lemma 8 (Inversion for ruleGDS-Both)DuoTyping/GFSubKernelUnionInter.v invChooseLemma 4 (Duality) DuoTyping/GFSubKernelUnionInter.v sym1Lemma 9 (F∧∨k<:NarrowingLemma)Monotyping/FSubKernalUnionInter.v sub_narrowingLemma 10 (F∧∨k♦ NarrowingLemma)DuoTyping/GFSubKernelUnionInter.v sub_narrowingLemma 11 (Type Preserva-tion)DuoTyping/GFSubKernelUnionInter.v preservation_resultLemma 12 (Progress) DuoTyping/GFSubKernelUnionInter.v progress_result

The Duality of Subtyping (Artifact)

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The Duality of Subtyping (Artifact)

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